You may have seen in a circus a motorcyclist driving in vertical loops inside a 'death well' (a hollow spherical chamber with holes, so the spectators can watch from outside). What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m ?

Question

You may have seen in a circus a motorcyclist driving in vertical loops inside a 'death well' (a hollow spherical chamber with holes, so the spectators can watch from outside). What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m ? (A) 12 ms -1 (B) 16 ms -1 (C) 20 ms -1 (D) 24 ms -1

Tardigrade Admin · Accepted Answer

At the uppermost point, N+m g=(m v/R), where N is the normal force (downwards) on the motorcyclist by the ceiling of the chamber. The minimum possible speed at the upper most point corresponds to N=0 ⇒ V min =√R g=√25 × 10 ≈ 16 ms -1

$12 m s^{- 1}$

$16 m s^{- 1}$

$20 m s^{- 1}$

$24 m s^{- 1}$

At the uppermost point, $N + m g = \frac{m v}{R}$ , where $N$ is the normal force (downwards) on the motorcyclist by the ceiling of the chamber. The minimum possible speed at the upper most point corresponds to $N = 0$
$\Rightarrow V_{m i n} = R g = 25 \times 10 \approx 16 m s^{- 1}$

12ms−1

16ms−1

20ms−1

24ms−1

At the uppermost point, N+mg=Rmv​, where N is the normal force (downwards) on the motorcyclist by the ceiling of the chamber. The minimum possible speed at the upper most point corresponds to N=0 ⇒Vmin​=Rg​=25×10​≈16ms−1

$12 m s^{- 1}$

$16 m s^{- 1}$

$20 m s^{- 1}$

$24 m s^{- 1}$

At the uppermost point, $N + m g = \frac{m v}{R}$ , where $N$ is the normal force (downwards) on the motorcyclist by the ceiling of the chamber. The minimum possible speed at the upper most point corresponds to $N = 0$
$\Rightarrow V_{m i n} = R g = 25 \times 10 \approx 16 m s^{- 1}$